1. Field of the Invention
The present invention relates to a polarization mode dispersion (PMD) compensator which is used to countermeasure signal distortion due to PMD for high-speed optical signals in the case the transmission distance or bit-rate is limited by the PMD of the transmission span (transmission line).
2. Description of the Related Art
The demand for higher capacity of optical transmission systems is increasing continuously. To increase the amount of data which can be transmitted in a specific amount of time through one optical fiber two methods exist in principal. While one method is wavelength division multiplexing (WDM), the other method is time division multiplexing (TDM).
To realize data-rates in the order of several Terabit/s a combination of TDM and WDM has to be used. Decreasing the number of channels in a WDM system while increasing the bit-rate each channel transports has several advantages. Past systems operated with 2.5 Gbit/s, current systems make use of 10 Gbit/s per channel and future systems will operate with 40 Gbit/s or even higher data-rates.
But with increasing data-rates a phenomenon, the so called polarization mode dispersion (PMD), becomes a transmission distance limiting physical property of an optical fiber. A PMD value of e.g. 5 ps does not affect a signal with a data-rate of 2.5 Gbit/s with a bit-duration of 400 ps in the case nonreturn-to-zero (NRZ) modulation format is used. But the same PMD value of 5 ps can contribute to signal distortion in the case of 10 Gbit/s signals (NRZ bit-duration equals 100 ps) and highly distorts a 40 Gbit/s signal (NRZ bit-duration equals 25 ps).
Even more worse, PMD is a statistical property due to the environmental dependence of birefringence and mode-coupling of a single-mode fiber. This means that, with some probability, the instantaneous differential group delay (DGD) can be much higher or lower than the mean DGD, i.e. PMD, of the fiber. While the instantaneous DGD is just the so called 1st-order PMD which follows a Maxwellian probability distribution, additionally higher-order PMD with an own statistical distribution due to the random mode-coupling exists.
Those are for example the DGD slope and the rotation rate of the principal states of polarization (PSP), being the 2nd-order PMD coefficients. For those who are skilled in the art, it is well known that several definitions of higher-order PMD exist. It is to be emphasized here, that in the case a signal experiences unacceptable high distortion due to accumulated PMD over the desired transmission distance, an active and adaptively adjustable compensation method is required to countermeasure this type of signal degradation.
Beside electrical and hybrid electric-optical compensation schemes all-optical schemes have been proposed. Among them, the all-optical compensation schemes will be discussed in the following.
All compensation schemes require a distortion analyzing device at the receiver side. The distortion analyzing device provides feedback to a control logic with a dedicated algorithm to adaptively adjust the parameters of a compensating device such that the signal experiences a minimum distortion. In general one can classify all-optical 1st-order PMD compensation schemes into the following three categories:
1. Polarization converter located at the transmitter side
FIG. 1 shows a system including this type of compensator. The system includes a transmitter 11 (Tx), a polarization converter 12 (PC), a transmission span 13, a receiver 14 (Rx) and a distortion analyzer 15.
In this system the distortion analyzer 15 analyzes distortion of an optical signal on the transmission span 13 and outputs a feedback signal to the polarization converter 12. According to the feedback signal the polarization converter 12 adaptively adjusts the input state of polarization to one of the two input PSP of the transmission span 13 (T. Ono, Y. Yano, L. D. Garrett, J. A. Nagel, M. J. Dickerson, and M. Cvijetic, “10 Gb/s PMD compensation filed experiment over 452 km using principal state transmission method,” OFC'99, paper PD44, 1999).
The compensator makes use of the fact that in the case the signal's state of polarization is aligned to one of the input PSP of the transmission span, the output state of polarization does not depend on wavelength to the first order. This further implies that under this launch condition the signal experiences least distortion.
2. Polarization converter followed by a polarization maintaining fiber (PMF) located at the receiver side
FIG. 2 shows a system including this type of compensator. The system includes the transmitter 11, the transmission span 13, the receiver 14, a polarization converter 21, a PMF 22 and a distortion analyzer 23. The polarization mode dispersion compensator (PMDC) consists of the polarization converter 21 and the PMF 22.
In this system the polarization converter 21 has to adaptively adjust the input principal state of polarization (PSP) of the concatenated transmission span 13 and PMDC to the state of input polarization (C. Francia, F. B. Bruyère, J. P. Thiéry, and D. Penninckx, “Simple dynamic polarisation mode dispersion compensator,” Electronics Letters, Vol. 35, No. 5, pp. 414-415, 1999; H. Ooi, Y. Akiyama, and G. Ishikawa, “Automatic polarization-mode dispersion compensation in 40-Gbit/s transmission,” OFC'99, paper WE5, pp. 86-88, 1999).
This shows good results until the instantaneous DGD of the transmission span is lower than a value being somewhat lower than the DGD of the PMDC's PMF. If the instantaneous DGD of the transmission span becomes higher than this value or exceeds the PMDC's PMF DGD value, a better method is to adjust the fast eigenstate of the PMF to the slow output PSP of the transmission span. Here, an eigenstate represents a characteristic of a medium and a state of polarization represents a characteristic of an optical signal or light.
Under those circumstances the transmission span's DGD is partly compensated for. The residual DGD of the concatenated transmission span and PMDC is the difference between the instantaneous DGD of the transmission span and the DGD of the PMF.
3. Polarization converter followed by a polarization beam splitter (PBS), an adjustable differential group delay line and a polarization beam combiner (PBC) located at the receiver side
FIG. 3 shows a system including this type of compensator. The system includes the transmitter 11, the transmission span 13, the receiver 14, a polarization converter 31, a PBS 32, an adjustable delay 33, a PBC 34 and a distortion analyzer 35.
In this system the polarization converter 31 has to adaptively adjust its fast eigenstate of polarization to the slow output PSP of the transmission span and, furthermore, adjust its DGD to the instantaneous DGD of the transmission span (F. Heismann, D. A. Fishman, and D. L. Wilson, “Automatic compensation of first-order polarization mode dispersion in a 10 Gb/s transmission system,” ECOC'98, pp. 529-530, 1998).
All of the above mentioned schemes to countermeasure signal distortion due to PMD only compensate for so called 1st-order PMD. They do not take into account that the DGD and the PSP are functions of wavelength.
FIGS. 4, 5 and 6 show typical functions of the DGD over wavelength, respectively, of fibers with PMD=5, 10 and 20 ps. In FIGS. 4, 5 and 6, the functions of the DGD are shown in a range of wavelength between 1545 nm and 1555 nm. FIGS. 7, 8 and 9 show typical variation of the PSP over wavelength, respectively, of fibers with PMD=5, 10 and 20 ps. In FIGS. 7, 8 and 9, the variation of the PSP are shown in a range of wavelength λ between 1545 nm and 1555 nm at 0.01-nm intervals using the Poincaré sphere representation. A black point represents a point on the front of the sphere, while a white point represents a point on the back of it. The presented graphs of the DGD and the PSP are taken from simulation studies for clarity reasons.
The spectral width of a modulated signal is not infinitely small. While the spectral component at the center wavelength of a modulated signal does not experience distortion due to PMD after 1st-order compensation, the other spectral components do (C. D. Poole and R. E. Wagner, “Phenomenological approach to polarisation dispersion in long single-mode fibers,” Electronics Letters, Vol. 22, No. 19, pp. 1029-1030, 1986). Even more worse, the compensation schemes shown in FIGS. 2 and 3, which are located at the receiver side, compensate for the DGD at the center wavelength but add additional PMD for the spectral components being apart from the center wavelength.
To compensate also for so called higher-order PMD, the PMD characteristic of the compensation scheme must reversely match the PMD characteristic of the transmission span (R. Noé, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schöpflin, C. Glingener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch, and W. Haase, “Polarization mode dispersion compensation at 10, 20, and 40 Gb/s with various optical equalizers,” Journal of Lightwave Technology, Vol. 17, No. 9, 1999).
For the above shortly discussed 1st-order compensation schemes this can only be fulfilled for the center wavelength of the signal. To further improve the compensation performance by means of matching the PMD characteristic of the transmission span for all or at least the spectral components of the signal near the center wavelength, multi-stage PMD compensation schemes have been proposed.
Those are either composed of stages comprising a polarization converter and a variable delay line (D. A. Fishman, F. L. Heismann, and D. L. Wilson, “Method and apparatus for automatic compensation of first-order polarization mode dispersion (PMD),” U.S. Pat. No. 5,930,414) or a polarization converter and a fixed DGD (e.g. PMF) (S. Hinz, D. Sandel, M. Yoshida-Dierolf, R. Noé, R. Wessel, and H. Suche, “Distributed fiberoptic PMD compensation of a 60 ps differential group delay at 40 Gbit/s,” ECOC'99, pp. II 136-II 137, 1999).
FIG. 10 shows a system according to the former multi-stage PMD compensation scheme. This system includes 1st through nth compensators 41 and a distortion analyzer 42. Each of the compensators 41 consists of the polarization converter 31, the PBS 32, the adjustable delay 33 and the PBC 34 shown in FIG. 3. While FIG. 11 shows a system according to the latter multi-stage PMD compensation scheme. This system includes 1st through nth compensators 51 and a distortion analyzer 52. Each of the compensators 51 consists of the polarization converter 21 and the PMF 22 shown in FIG. 2.
To those who are skilled in the art, it is well understood that with an increasing number of stages the principle performance will increase. The more stages are used the better the PMD characteristic of the transmission span can be matched by the PMDC. But also the complexity due to the added degrees of freedom increases. The increased complexity will make it difficult to adaptively adjust the PMD characteristic of the compensation scheme. A mathematical description of PMD makes use of the so called PMD vector (J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” PNAS, Vol. 97, No. 9, pp. 4541-4550, 2000). The PMD vector {right arrow over (P)} can be separated into its two components τ (DGD) and {right arrow over (p)} (PSP) as follows.{right arrow over (P)}(ω)=τ(ω)·{right arrow over (p)}(ω)  (1)
While the DGD is also referred to as 1st-order PMD, 2nd-order PMD parameters are calculated by deriving {right arrow over (P)} with respect to the frequency ω as follows.                                           ⅆ                                          P                →                            ⁡                              (                ω                )                                                          ⅆ            ω                          =                                                                              ⅆ                  τ                                ⁢                                                                   ⁢                                  (                  ω                  )                                                            ⅆ                ω                                      ·                                          p                →                            ⁡                              (                ω                )                                              +                                    τ              ⁡                              (                ω                )                                      ·                                          ⅆ                                                      p                    →                                    ⁡                                      (                    ω                    )                                                                              ⅆ                ω                                                                        (        2        )            
The 2nd-order PMD is composed of a polarization dependent chromatic dispersion                     ⅆ        τ            ⁢                           ⁢              (        ω        )                    ⅆ      ω        ⁢           [      ps    ⁢          /        ⁢    nm    ](DGD slope) component and the rotation rate of the PSP                     ⅆ                              p            →                    ⁡                      (            ω            )                                      ⅆ        ω              ⁢                   [          rad      ⁢              /            ⁢      nm        ]    .Rotation rate of the PSP is measured in units of radians per nanometer. It leads to the effect that every spectral component of a modulated signal has its own associated PSP. Dependent on the state of input polarization of the modulated signal, the power of every spectral component is split into its associated two PSP (ratio of power splitting depends on angle between the state of input polarization of the signal and the PSP of the fiber at the respective wavelength), whereby the two polarization components experience a DGD.
Further derivation leads to 3rd-order PMD parameters as follows.                                                         ⅆ              2                        ⁢                                          P                →                            ⁡                              (                ω                )                                                          ⅆ                          ω              2                                      =                                                                                                  ⅆ                    2                                    ⁢                  τ                                ⁢                                                                   ⁢                                  (                  ω                  )                                                            ⅆ                                  ω                  2                                                      ·                                          p                →                            ⁡                              (                ω                )                                              +                      τ            ⁢                                                   ⁢                                          (                ω                )                            ·                                                                    ⅆ                    2                                    ⁢                                                            p                      →                                        ⁡                                          (                      ω                      )                                                                                        ⅆ                                      ω                    2                                                                                +                      2            ·                                                            ⅆ                  τ                                ⁢                                                                   ⁢                                  (                  ω                  )                                                            ⅆ                ω                                      ·                                          ⅆ                                                      p                    →                                    ⁡                                      (                    ω                    )                                                                              ⅆ                ω                                                                        (        3        )                                          ⅆ          2                ⁢        τ            ⁢                           ⁢              (        ω        )                    ⅆ              ω        2              ⁢           ⁢  and  ⁢           ⁢                    ⅆ        2            ⁢                        p          →                ⁡                  (          ω          )                            ⅆ              ω        2            represent the chromatic dispersion slope and the change rate of PSP rotation, respectively. In the case the vectorial sum of the transmission span's PMD vector and the PMD vector of a PMD compensator is zero at least within the spectral bandwidth of the modulated signal, signal distortion due to PMD is perfectly mitigated.
Because perfect mitigation requires a huge number of DGD sections interleaved by polarization converters (Y. Li, A. Eyal, and A. Yariv, “Higher order error of discrete fiber model and asymptotic bound on multistaged PMD compensation,” Journal of Lightwave Technology, Vol. 18, No. 9, pp. 1205-1213, 2000), control speed is limited and total size and number of required components makes this type of perfect or nearly perfect compensation scheme unattractive at least from an economical point of view.
Fewer stages will ever leave a residual distortion due to higher-order PMD which they are not designed to compensate for (P. Ciprut et al., “Second-order polarization mode dispersion: Impact on analog and digital transmissions,” Journal of Lightwave Technology, Vol. 16, No. 5, pp. 757-771, 1998; C. Francia, F. Bruyère, D. Penninckx, and M. Chbat, “PMD second-order effects on pulse propagation in single-mode optical fibers,” IEEE Photonics Technology Letters, Vol. 10, No. 12, pp. 1739-1741, 1998). But for a given transmission span with a specific and not-too-high PMD value, those schemes are able to partly match the PMD vector reversely. This leads to some residual but reduced penalty which has to be taken into account for system design considerations.
FIG. 12 gives a clear image for covered ranges of occurring 1st- (DGD) and 2nd-order (PSP rotation rate) PMD parameters in real fibers. For single mode fibers (SMFs) with PMD values of 4, 8 and 16 ps, 5×105 realizations of a realistic fiber model with 1000 linear birefringent segments has been investigated (W. Weiershausen, R. Leppla, F. Küppers, and H. Schöll, “Polarization-mode dispersion in fibre transmission: Theoretical approach, impact on systems, and suppression of signal-degradation effects,” ECOC'99, pp. II 130-II 133, 1999). FIG. 12 shows the PSP rotation rate versus the instantaneous DGD. While the instantaneous DGD follows the well known Maxwellian probability distribution function (not shown here), the maximum occurring PSP rotation rate decreases with increasing DGD.